Just problem number 1 please! :) Consider the data in Table 1: (a) Determine the
ID: 3295325 • Letter: J
Question
Just problem number 1 please! :)
Consider the data in Table 1: (a) Determine the equation of the line that best fits these points. (b) Determine the 95% confidence intervals for the coefficients of the line. (c) Determine the mean value of y corresponding to x = 0.75 and the confidence interval for this value of y. (d) Determine the value of y corresponding to x = 0.75 and the confidence interval for this value of y (e) Determine the value of y corresponding to x = 1.1 and the confidence interval for this value of y. Problem 3.1 Problem 5.4 Problem 5.6 Problem 5.8 Problem 7.2 Problem 8.2 Problem 9.1 Problem 9.3Explanation / Answer
Q.1 (a) Let say the least squares regression line equation is y^ = a + bx. to get the value of line constants,we shall require the value of x, y, x2 , y2 ,xy. This table will help us to find it.
or line equation y^ = a + bx
a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]
a = [12.7 * 3.64 - 4.2 * 5.52] / [7 * 3.64 - 4.22]
a =23.044/ 7.84 = 2.9393
b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]
b = [7 * 5.52 - 4.2 * 12.7 / [ 7 * 3.64 - 4.22 ]
b = -14.7/ 7.84 = -1.875
so line equation is y^ = -1.875x + 2.9393
(b) 95% confidence interval for the coeffieints.
Standard error of the regression se0 = sqrt [(y-y')2 / (n-2)] = sqrt [0.291/5] = 0.2413
Standard error of Intercept sa = se0 sqrt [1/n + (xbar )2 / (xi -xbar )2 ]
sa = 0.2413 * sqrt [ 1/7 + 0.62 /1.12] = 0.1644
95% confidence interval = a + t0.025,5 Sa = = 2.9393 +- 2.570 * 0.1644 = (2.5166 , 3.3620)
Standard error of slope sb = se0 /sqrt [(n-1)sx
sb = 0.228
95% confidence interval = b + t0.025,5 Sb = -1.875 +- 2.570 * 0.228 = (-2.461, -1.289)
(d) x= 0.75 , y^ = -1.875 * 0.75 + 2.9393 = 1.533
95% confidence interval for y (0.75) = y^ +- tcrtic se
se = sxy sqrt [ 1/n + (x - xbar )2 /SSx ] = 0.2413 * sqrt [1/7 + (0.75 - 0.6)2 / 1.12]
se = 0.0974
y (0.75) = y^ +- tcrtic se = 1.533 +- 2.570 * 0.0974 = (1.2827, 1.7833)
(e)
x= 1.1 , y^ = -1.875 * 1.1 + 2.9393 = 0.877
95% confidence interval for y (1.1) = y^ +- tcrtic se
se = sxy sqrt [ 1/n + (x - xbar )2 /SSx ] = 0.2413 * sqrt [1/7 + (1.1 - 0.6)2 / 1.12]
se = 0.146
y (0.75) = y^ +- tcrtic se = 0.877 +- 2.570 * 0.146 = (0.5018, 1.2522)
x y x^2 y^2 xy 0 3.2 0 10.24 0 0.2 2.4 0.04 5.76 0.48 0.4 2.2 0.16 4.84 0.88 0.6 1.5 0.36 2.25 0.9 0.8 1.6 0.64 2.56 1.28 1 0.9 1 0.81 0.9 1.2 0.9 1.44 0.81 1.08 sum 4.2 12.7 3.64 27.27 5.52Related Questions
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